A squared autumn ENSO term did not show a clear gain in U.S. winter precipitation predictions for 1981–2025

We tested whether a squared autumn Niño 3.4 term improves winter precipitation prediction beyond a linear term. The test used NOAA data for 344 climate divisions in the contiguous United States. Each winter prediction used only earlier winters to fit the model. Across 45 test winters in 1981–2025, the squared term increased average normalized mean squared error by 0.92%. A paired 5-year block interval for error reduction was -3.53% to +1.85%. The West Coast estimate showed a 5.14% reduction, but its interval also crossed zero. Removing the time trend, using log precipitation, and changing the block length did not give a clear national gain. These revised-data hindcasts do not establish real-time skill, a physical mechanism, or the absence of nonlinear rainfall responses. The package includes source code, checked data hashes, seasonal inputs, all predictions, and uncertainty estimates.

ENSO · seasonal prediction · precipitation · forward validation · null result